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NEW YORK — Wall Street began the second quarter with a big rally Tuesday as investors rushed back into stocks, optimistic that the worst of the credit crisis has passed and that the economy is faring better than expected. The Dow Jones industrials surged nearly 400 points, and all the major indexes were up more than 3 percent.

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Financial stocks were among the big winners after Lehman Brothers Holdings Inc. and Switzerland’s UBS AG issued new shares to help bolster their balance sheets. With that upbeat news and a fresh quarter ahead of them, investors appear quite willing to make some bets that the worst of the damage from the nation’s credit struggles has been felt. Moreover, the banks’ moves buttressed the view that financial services companies are taking aggressive action to improve their capital bases and stave off the potential of a collapse similar to Bear Stearns Cos.

Analysts believe there must be a recovery in bank and brokerage stocks to lead major stock indexes higher. Some of the biggest financial players had their biggest moves of the year Tuesday — Citigroup Inc. shot up 11 percent, JPMorgan Chase & Co. rose 9 percent, and Lehman surged 18 percent.

“Investors have a difficult time making decisions about the stock market if they don’t have confidence in major financial institutions, so there’s been a lot of sideline cash,” said Richard Cripps, chief market strategist for Stifel Nicolaus. “The extreme conditions that we’ve seen here over the past few months has been missing that confidence ... but that appears to be changing, and we’re seeing the response.”

Meanwhile, Wall Street got another boost when the Institute for Supply Management said its March index of national manufacturing activity rose to a reading of 48.6 — indicating a contraction, but a slower one than in February and tamer than many analysts had predicted. Government data on construction spending for February also came in better than expected.

At the close of trading, the Dow rose 391.47, or 3.19 percent, to 12,654.47.

The advance was in contrast to a lackluster session on Monday, where stocks managed a moderate gain in the final session of a dismal first quarter. Major indexes ended the first three months of 2008 with massive losses, marking the worst period since the third quarter of 2002 when Wall Street was approaching the lowest point of a protracted bear market.

Renewed enthusiasm that the credit crisis might be waning was also felt in the Treasury market, where government securities fell as investors withdrew money to take bets on stocks. The 10-year Treasury note’s yield, which moves opposite its price, rose to 3.55 percent from 3.43 percent late Monday.

In addition to hopes about the financial sector, Wall Street was relieved to see the feeble dollar regain some strength against the euro. The euro fell to $1.5596 from $1.5785 late Monday in New York.

And there was also optimism that commodities prices, which have hit historic highs in recent months, have begun to retreat. Crude fell 60 cents to settle at $100.98 on the New York Mercantile Exchange after earlier falling below $100. Meanwhile, gold dropped back below $900 an ounce.

“This is a nice way to begin the second quarter,” said Todd Leone, managing director of equity trading at Cowen & Co. “All the financials are up big, and there’s a sense that things are turning. We definitely have not seen the last of the credit crisis, but we’re getting closer.”

The stock rally was underpinned by the announcements from UBS and Lehman Brothers that they are boosting capital by issuing new stock. Shares of banks and brokerages hovered near multiyear lows in recent months as investors feared heavy losses from investments tied to subprime mortgages would be overwhelming.

Earlier this month, widespread concerns about Bear Stearns’ financial position forced the investment bank to sell itself at a bargain basement price to JPMorgan in a deal engineered by the Federal Reserve — and that stoked fears that other investment houses might follow.

JPMorgan rose $4.05, or 9.4 percent, to $47; while Bear Stearns was up 36 cents, or 3.4 percent, to $10.85 — slightly above the $10 per share acquisition price.

UBS, one of Europe’s biggest banks, said it will issue up to $15 billion in new stock and that its chairman, Marcel Ospel, had quit. Investors chose to look past the bank’s announcement that it will take a fresh $19 billion write-down due to additional declines in the value of its mortgage assets and other credit instruments, following an $18 billion write-down last year. Its shares surged $4.21, or 14.6 percent, to $33.01 in trading on the New York Stock Exchange.

Lehman Brothers, dogged by speculation it might reveal losses big enough to cripple the company, on Tuesday raised $4 billion of capital on Tuesday to stymie questions about its financial stability. Lehman rose $6.70, or 17.8 percent, to $44.34.